This research is intended to provide a numerical algorithm for solving a one-dimensional inverse heat conduction problem. The given heat conduction equation, the boundary conditions and the initial condition are presented in a dimensionless form. A numerical approach combining the use of the finite difference method with the solution of Ordinary Differential Equation (ODE) is proposed for the determination of temperature distribution in an Inverse Heat Conduction Problem (IHCP). The leastsquares method is adopted to find the solution. Results show that an excellent estimation can beobtained within a couple of minute’s CPU time at pentium IV-2.4 GHz PC.